Related papers: Linguistic Geometries for Unsupervised Dimensional…

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…

Accurate volume estimation of objects from visual data is a long-standing challenge in computer vision with significant applications in robotics, logistics, and smart health. Existing methods often rely on complex 3D reconstruction…

Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the…

Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for…

The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden…

In this paper, we present Language Model as Visual Explainer LVX, a systematic approach for interpreting the internal workings of vision models using a tree-structured linguistic explanation, without the need for model training. Central to…

The rapidly growing ecosystem of Large Language Models (LLMs) makes it increasingly challenging to manage and utilize the vast and dynamic pool of models effectively. We propose LOCUS, a method that produces low-dimensional vector…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the…

Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…

One of the main methods for computational interpretation of a text is mapping it into a vector in some embedding space. Such vectors can then be used for a variety of textual processing tasks. Recently, most embedding spaces are a product…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

Dimensionality reduction techniques map values from a high dimensional space to one with a lower dimension. The result is a space which requires less physical memory and has a faster distance calculation. These techniques are widely used…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…

Visualization is a crucial step in exploratory data analysis. One possible approach is to train an autoencoder with low-dimensional latent space. Large network depth and width can help unfolding the data. However, such expressive networks…

This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…

Semantic text representation is a fundamental task in the field of natural language processing. Existing text embedding (e.g., SimCSE and LLM2Vec) have demonstrated excellent performance, but the values of each dimension are difficult to…